Rewrite as a simplified fraction. ${2.6\overline{7} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 267.7777...\\ 10x &= 26.7777...\end{align*}}$ Subtracting the two equations, we have: ${90x = 241}$ ${x = \dfrac{241}{90}} \text{or} {2 \dfrac{61}{90}}$